Explanation: When an AC voltage supplies a vacuum tube's filament, the potential along the filament wire varies sinusoidally with respect to ground. If the plate and grid return circuits were connected directly to one end of the filament, this AC voltage variation would be injected into these sensitive circuits. This injected AC voltage, typically at the power line frequency (e.g., 60 Hz), acts as an unwanted signal, causing "hum" which modulates the desired radio frequency or audio frequency signals passing through the tube. A center tap on the filament transformer secondary (or a resistive voltage divider across the filament) provides an electrical reference point that is at the *average* potential of the filament. Connecting the grid and plate return circuits to this center tap minimizes the AC potential difference between the cathode (heated by the filament) and these circuits, effectively canceling out most of the hum voltage and preventing it from modulating the normal signals.